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<div class="section">
<div class="titlepage"><div><div><h4 class="title">
<a name="math_toolkit.stat_tut.overview.objects"></a><a class="link" href="objects.html" title="Distributions are Objects">Distributions
        are Objects</a>
</h4></div></div></div>
<p>
          Each kind of distribution in this library is a class type - an object,
          with member functions.
        </p>
<div class="tip"><table border="0" summary="Tip">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../../../../../doc/src/images/tip.png"></td>
<th align="left">Tip</th>
</tr>
<tr><td align="left" valign="top"><p>
            If you are familiar with statistics libraries using functions, and 'Distributions
            as Objects' seem alien, see <a class="link" href="../weg/nag_library.html" title="Comparison with C, R, FORTRAN-style Free Functions">the
            comparison to other statistics libraries.</a>
          </p></td></tr>
</table></div>
<p>
          <a class="link" href="../../../policy.html" title="Chapter 22. Policies: Controlling Precision, Error Handling etc">Policies</a> provide optional fine-grained control
          of the behaviour of these classes, allowing the user to customise behaviour
          such as how errors are handled, or how the quantiles of discrete distributions
          behave.
        </p>
<p>
          Making distributions class types does two things:
        </p>
<div class="itemizedlist"><ul class="itemizedlist" style="list-style-type: disc; ">
<li class="listitem">
              It encapsulates the kind of distribution in the C++ type system; so,
              for example, Students-t distributions are always a different C++ type
              from Chi-Squared distributions.
            </li>
<li class="listitem">
              The distribution objects store any parameters associated with the distribution:
              for example, the Students-t distribution has a <span class="emphasis"><em>degrees of
              freedom</em></span> parameter that controls the shape of the distribution.
              This <span class="emphasis"><em>degrees of freedom</em></span> parameter has to be provided
              to the Students-t object when it is constructed.
            </li>
</ul></div>
<p>
          Although the distribution classes in this library are templates, there
          are typedefs on type <span class="emphasis"><em>double</em></span> that mostly take the usual
          name of the distribution (except where there is a clash with a function
          of the same name: beta and gamma, in which case using the default template
          arguments - <code class="computeroutput"><span class="identifier">RealType</span> <span class="special">=</span>
          <span class="keyword">double</span></code> - is nearly as convenient).
          Probably 95% of uses are covered by these typedefs:
        </p>
<pre class="programlisting"><span class="comment">// using namespace boost::math; // Avoid potential ambiguity with names in std &lt;random&gt;</span>
<span class="comment">// Safer to declare specific functions with using statement(s):</span>

<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">beta_distribution</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">binomial_distribution</span><span class="special">;</span>
<span class="keyword">using</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">students_t</span><span class="special">;</span>

<span class="comment">// Construct a students_t distribution with 4 degrees of freedom:</span>
<span class="identifier">students_t</span> <span class="identifier">d1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>

<span class="comment">// Construct a double-precision beta distribution</span>
<span class="comment">// with parameters a = 10, b = 20</span>
<span class="identifier">beta_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">d2</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="number">20</span><span class="special">);</span> <span class="comment">// Note: _distribution&lt;&gt; suffix !</span>
</pre>
<p>
          If you need to use the distributions with a type other than <code class="computeroutput"><span class="keyword">double</span></code>, then you can instantiate the template
          directly: the names of the templates are the same as the <code class="computeroutput"><span class="keyword">double</span></code> typedef but with <code class="computeroutput"><span class="identifier">_distribution</span></code>
          appended, for example: <a class="link" href="../../dist_ref/dists/students_t_dist.html" title="Students t Distribution">Students
          t Distribution</a> or <a class="link" href="../../dist_ref/dists/binomial_dist.html" title="Binomial Distribution">Binomial
          Distribution</a>:
        </p>
<pre class="programlisting"><span class="comment">// Construct a students_t distribution, of float type,</span>
<span class="comment">// with 4 degrees of freedom:</span>
<span class="identifier">students_t_distribution</span><span class="special">&lt;</span><span class="keyword">float</span><span class="special">&gt;</span> <span class="identifier">d3</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>

<span class="comment">// Construct a binomial distribution, of long double type,</span>
<span class="comment">// with probability of success 0.3</span>
<span class="comment">// and 20 trials in total:</span>
<span class="identifier">binomial_distribution</span><span class="special">&lt;</span><span class="keyword">long</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">d4</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="number">0.3</span><span class="special">);</span>
</pre>
<p>
          The parameters passed to the distributions can be accessed via getter member
          functions:
        </p>
<pre class="programlisting"><span class="identifier">d1</span><span class="special">.</span><span class="identifier">degrees_of_freedom</span><span class="special">();</span>  <span class="comment">// returns 4.0</span>
</pre>
<p>
          This is all well and good, but not very useful so far. What we often want
          is to be able to calculate the <span class="emphasis"><em>cumulative distribution functions</em></span>
          and <span class="emphasis"><em>quantiles</em></span> etc for these distributions.
        </p>
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        Distributed under the Boost Software License, Version 1.0. (See accompanying
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